I tried to divide (t-a) with (t^2 - 3at + a^2), but in the end I had a^2 left, so I came up with no solution. I have tried once again to use the quadratic formula -- and this time the answer seems more plausible... I have tried to set a to 5 and plot it on my ti-83 and now the roots are okay. Strange how I found it to be wrong the first time.

hehe.. if you divide your quadratic equation by a and got a remainder, then a must be a unique eigenvalue of your matrix..

hmm, for some reasons, i am active because it saturday here and i have a lot of time checking the site.. but during weekdays, i am in school almost the whole day that is why when i come back home, it is already late and i have to sleep for tomorrow.. Ü